Several medical imaging modalities are based on the reconstruction of tomographic images from projective line-integral measurements. For these imaging modalities, typical iterative implementations spend most of the computation performing two line projection operations. The forward projection accumulates image data along projective lines. The back-projection distributes projection values back into the image data uniformly along the same lines. Both operations can include a weighting function called a “projection kernel”, which defines how much any given voxel contributes to any given line. For instance, a simple projection kernel is 1 if the voxel is traversed by the line, zero otherwise.
As a result of the increasing complexity of medical scanner technology, the demand for fast computation in image reconstruction has exploded. Fortunately, line projection operations are independent across lines and voxels and are computable in parallel. Early after the introduction of the first graphics acceleration cards, texture mapping hardware was proposed as a powerful tool for accelerating the projection operations for sinogram datasets.
In a sinogram, projective lines are organized according to their distance from the isocenter and their angle. FIG. 2 shows an example of sinogram data. Here, a set of lines 204 emanates from a source 202 and passes through an object 104. Integrated responses along each of the lines are measured by numerous detectors (not shown) at the periphery of the system chamber 102. The linear mapping between the coordinates of a point in the reconstructed image and its projection in each sinogram view can be exploited using linear interpolation hardware built into the texture mapping units, which is the basis for almost every GPU implementation. The article by Xu et al., “Accelerating popular tomographic reconstruction algorithms on commodity PC graphics hardware” (IEEE Trans. Nuc. Sci. 52(3) (2005) p654) is an example of such a GPU approach.
While many tomographic imaging modalities such as X-ray computed tomography (CT) acquire projection data of inherent sinogram nature, others—in particular, positron emission tomography (PET)—are based on spatially-random measurements.
In clinical practice, PET scanners are used mainly in the management of cancer. The purpose of a PET scan is to estimate the biodistribution of a molecule of interest—for instance, a molecule retained by cancerous cells. A radioactive version of the molecule is administered to the patient and distributes throughout the body according to various biological processes. Radioactive decay followed by positron-electron annihilation results in the simultaneous emission of two anticollinear high-energy photons. These photons are registered by small detector elements arranged around the measurement field. Detection of two photons in near temporal coincidence indicates that a decay event likely occurred on the line (called line of response, or LOR) that joins the two detector elements involved. The stream of coincidence events is sent to a data acquisition computer for image reconstruction.
Some PET systems have so called time-of-flight (TOF) capabilities. In these systems, the difference in arrival time of the two high-energy photons is measured with high accuracy. This measurement is used to estimate the rough position of the radioactive decay along the LOR. Included in the image reconstruction, the TOF information can improve image quality and quantitative accuracy, thereby improving lesion detectability.
FIG. 1 shows an example of this kind of interaction geometry. Here object 104 is the patient, and it is assumed that a coincidence event is detected by detectors 110 and 112 of the system. Numerous other detectors (not shown) would be present at the periphery of chamber 102 in a real system. From this observation, the annihilation event is known to have occurred somewhere on the line of response 108, e.g., at point 106. Each registered coincidence event will have its corresponding line of response, and in general there will be no organization or pattern in the obtained lines of response. Positron absorption and emission are random events, and the line of response orientation from each electron-positron annihilation event is also random. A processor 120 is employed to reconstruct an image of object 104 from the measured data.
Although coincidence events provide line-integral measurements of the tracer distribution, histogramming these events into a sinogram is often inefficient because the number of events recorded is much smaller than the number of possible measurements, and, therefore, the sinogram is sparsely filled. Instead, reconstruction is performed directly from the list-mode data, using algorithms such as list-mode ordered-subsets expectation-maximization (OSEM), a variation of the popular OSEM algorithm, itself an accelerated version of the EM algorithm. List-mode OSEM computes the maximum likelihood estimate by iteratively applying a sequence of forward and back-projection operations along a list of lines. The forward and back-projection operations are performed along individual lines, taken from a list representing recorded coincidence events. The image is typically initialized with ones.
List-mode OSEM is a computationally-demanding algorithm that cannot be implemented using GPU texture-mapping approaches because the linear mapping between image space and projection space does not apply to a list of randomly-oriented lines. Instead, lines must be processed individually, which raises new, complex challenges for a GPU implementation.
A previous implementation of list-mode OSEM using a GPU is described in US patent publication 2007/0201611 and in an article by Pratx et al. “Fast, accurate and shift-varying line projections for iterative reconstruction using the GPU” (IEEE Trans. Med. Image 28(3) (2009) p435), both of which are incorporated by reference in their entirety. In the cited work, the data write operations were performed by programming in the vertex shaders where the output is written. A rectangular polygon is drawn into the frame-buffer object so that it encompasses the intersection of the line with the slice.
However, it remains desirable to provide further improvements for list mode OSEM reconstruction implementations using GPUs.